Abstract
One effective method for analyzing complexity involves applying information measures to time series derived from observational data. Permutation entropy (PE) is one such measure designed to quantify the degree of disorder or complexity within a time series by examining the order relations among its values. PE is distinguished by its simplicity, robustness, and exceptionally low computational cost, making it a benchmark tool for complexity analysis. This text reviews the advantages and limitations of PE while exploring its diverse applications in hydrology from 2002 to 2025. Specifically, it categorizes the uses of PE across various subfields, including runoff prediction, streamflow analysis, water level forecasting, assessment of hydrological changes, and evaluating the impact of infrastructure on hydrological systems. By leveraging PE's ability to capture the intricate dynamics of hydrological processes, researchers can enhance predictive models and improve our understanding of water-related phenomena.